Emily had 35 as many pens as Raeann. The sum of the number of pens Emily and Raeann had was the same as the number of pens that Lucy had. After trading, Lucy gave 10% of her pens to Emily and received 20% of Raeann's pens. After that, Raeann continued to trade and increased her number of pens in the end by 20%, find the ratio of her number of pens to the sum of Emily's and Lucy's pens in the end.
| |
Emily |
Lucy |
Raeann |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 0.8 u |
- 0.8 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
3.8 u |
8.2 u |
4 u |
|
| Change 3 |
- 0.8 u |
+ 0.8 u |
|
| After 2 |
11.2 u |
4.8 u |
16 u |
Total number of pens that Emily and Raeann had at first
= 3 u + 5 u
= 8 u
Number of pens that Lucy had at first = 8 u
Number of pens that Lucy gave to Emily
= 10% x 8 u
=
10100 x 3 u
= 0.8 u
Number of pens that Lucy received from Raeann
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of pens that Raeann increased by when she continued to trade
= 20% x 4 u
=
20100 x 4 u
= 0.8 u
Number of pens that Emily and Lucy had in the end
= 3.8 u + 8.2 u - 0.8 u
= 11.2 u
In the end
Raeann : Emily and Lucy
4.8 : 11.2
480 : 1120
3 : 7
Answer(s): 3 : 7
